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Algebraic simplification in computer algebra: an analysis of bottom-up algorithms

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Casas, Rafael and Fernández Camacho, María Inés and Steyaert, Jean-Marc (1990) Algebraic simplification in computer algebra: an analysis of bottom-up algorithms. Theoretical Computer Science, 74 (3). pp. 273-298. ISSN 0304-3975

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Official URL: http://www.sciencedirect.com/science/article/pii/030439759090078V


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Abstract

We consider a class of simplification algorithms for algebraic and logical expressions which are of systematic use in computer algebra systems. This class is basically characterized by the fact that algorithms operate in a bottom-up recursive way on the expressions, i.e. start from the atomic terms—constants and variables—and perform the simplifications on larger and larger terms until the whole expression is ultimately proceeded; no backtracking or iterated process should intervene in the simplification. We show that under these quite general assumptions, it is possible to analyze precisely, and almost automatically, the average size of the resulting expressions—the gain in space—and the average time complexity of the process, which happens to be linear, whereas the worst-case behaviour is not in general.


Item Type:Article
Uncontrolled Keywords:Symbolic computation, algebraic computation; Mechanization of proofs and logical operations
Subjects:Sciences > Computer science
ID Code:20609
Deposited On:01 Apr 2013 13:59
Last Modified:09 Aug 2018 08:37

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